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Answer To The Gazebo Located In The Center Of A Circular Lawn Problem

GEOMETRY PROBLEMS – In this article, we are going to show the solution to the problem that goes “A gazebo is located in the center of a large, circular lawn with a diameter of 200 feet“.

The full problem asks:

A gazebo is located in the center of a large, circular lawn with a diameter of 200 feet. Straight paths extend from the gazebo to a sidewalk around the lawn. If two of the paths form a 75° angle, how far would you have to travel around the sidewalk to get from one path to the other? Round your answer to the nearest foot if necessary.

A Gazebo Is Located In The Center Of A Large, Circular Lawn (Answer)
Image from: Pinterest

The choices for the answer are:

A. 183 ft
B. 262 ft
C. 131 ft
D. 3,125 ft

Since we know that the gazebo is located in the center of a circular lawn we should be able to easily get the formula. The question also asks how far would you travel around the sidewalk to get from one path to another.

With this in mind, we could get the formula for the length of travel as L = (75*pi*100) / 180 (degrees)). In this formula, 75 is the angle and 100 is the radius of the circle (half of the diameter). Meanwhile, to get from one side of the circle to another, you need to travel 180 degrees.

With this, you get L = 130.83 which could be rounded off to 131 ft. This means C is the right answer.

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